Hence, x = 9 and y = 4 is the solution of given system of equations. Solving System of Equations Using Substitution Methodįor solving the system of equations using the substitution method given two linear equations in x and y, express y in terms x in one of the equations and then substitute it in 2nd equation. Let us understand 3 ways to solve a system of equations given the equations are linear equations in two variables. Similarly, for solving a system of equations in 3 variables, we will require at least 3 equations. To solve a system of equations in 2 variables, we need at least 2 equations. Infinite Many SolutionsĪ system of equations can have infinitely many solutions when there exists a solution set of infinite points for which L.H.S and R.H.S of an equation become equal, or in the graph straight lines overlap each other.Īny system of equations can be solved in different methods. No SolutionĪ system of equations has no solution when there exists no point where lines intersect each other or the graphs of equations are parallel. Similarly, for a system of linear equations in two variables, the unique solution is an ordered pair (x, y) which will satisfy both the equations in the system. Let understand the concept of a unique solution using a linear equation in one variable, 4x = 8 has a unique solution x = 2 for which the L.H.S is equal to the R.H.S. The unique solution of a system of equations means that there exists only one value for the variable or the point of intersection of the lines representing those equations, on substituting which, L.H.S and R.H.S of all the given equations in the system become equal.įor example, we know that a linear equation in one variable will always have one solution. There can be different types of solutions to a given system of equations, The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.

We compute the values of the unknown variables still balancing the equations on both sides. Solving a system of equations means finding the values of the variables used in the set of equations.

Two equation systems